Classification of the N=2, Z2 X Z2-symmetric type II orbifolds and their type II asymmetric duals

Using free world-sheet fermions, we construct and classify all the N=2, Z2 X Z2 four-dimensional orbifolds of the type IIA/B strings for which the orbifold projections act symmetrically on the left and right movers. We study the deformations of these models out of the fermionic point, deriving the partition functions at a generic point in the moduli of the internal torus T6=T2 X T2 X T2. We investigate some of their perturbative and non-perturbative dualities and construct new dual pairs of type IIA/type II asymmetric orbifolds, which are related non-perturbatively and allow us to gain insight into some of the non-perturbative properties of the type IIA/B strings in four dimensions. In particular, we consider some of the (non-)perturbative gravitational corrections.Comment: Latex, 47 pages, no figure

First Case of Systemic Coronavirus Infection in a Domestic Ferret (Mustela putorius furo) in Peru.

A domestic ferret from Lima, Peru, died after ten days of non-specific clinical signs. Based on pathology, immunohistochemistry and molecular analysis, ferret systemic coronavirus (FRSCV)-associated disease was diagnosed for the first time in South America. This report highlights the potential spread of pathogens by the international pet trade

Wireless Content Caching for Small Cell and D2D Networks

The fifth generation wireless networks must provide fast and reliable connectivity while coping with the ongoing traffic growth. It is of paramount importance that the required resources, such as energy and bandwidth, do not scale with traffic. While the aggregate network traffic is growing at an unprecedented rate, users tend to request the same popular contents at different time instants. Therefore, caching the most popular contents at the network edge is a promising solution to reduce the traffic and the energy consumption over the backhaul links. In this paper, two scenarios are considered, where caching is performed either at a small base station, or directly at the user terminals, which communicate using Device-to-Device (D2D) communications. In both scenarios, joint design of the transmission and caching policies is studied when the user demands are known in advance. This joint design offers two different caching gains, namely, the pre-downloading and local caching gains. It is shown that the finite cache capacity limits the attainable gains, and creates an inherent tradeoff between the two types of gains. In this context, a continuous time optimization problem is formulated to determine the optimal transmission and caching policies that minimize a generic cost function, such as energy, bandwidth, or throughput. The jointly optimal solution is obtained by demonstrating that caching files at a constant rate is optimal, which allows reformulation of the problem as a finite-dimensional convex program. The numerical results show that the proposed joint transmission and caching policy dramatically reduces the total cost, which is particularised to the total energy consumption at the Macro Base Station (MBS), as well as to the total economical cost for the service provider, when users demand economical incentives for delivering content to other users over the D2D links

XUV Opacity of Aluminum between the Cold-Solid to Warm-Plasma Transition

We present calculations of the free-free XUV opacity of warm, solid-density aluminum at photon energies between the plasma frequency at 15 eV and the L-edge at 73 eV, using both density functional theory combined with molecular dynamics and a semi-analytical model in the RPA framework with the inclusion of local field corrections. As the temperature is increased from room temperature to 10 eV, with the ion and electron temperatures equal, we calculate an increase in the opacity in the range over which the degree of ionization is constant. The effect is less pronounced if only the electron temperature is allowed to increase. The physical significance of these increases is discussed in terms of intense XUV-laser matter interactions on both femtosecond and picosecond time-scales.Comment: 4 pages, 3 figure

Examples of non-strong fuzzy metrics

Answering a recent question posed by Gregori et al. [On a class of completable fuzzy metric spaces, Fuzzy Sets and Systems 161 (2010), 2193-2205] we present two examples of non-strong fuzzy metrics (in the sense of George and Veeramani). © 2010 Elsevier B.V. All rights reserved.This research was supported by the Ministry of Science and Innovation of Spain under Grants MTM2009-12872-C02-01 and MTM2009-12872-C02-02. J. Gutierrez Garcia also acknowledges financial support from the University of the Basque Country under Grant GIU07/27.Gutiérrez García, J.; Romaguera Bonilla, S. (2011). Examples of non-strong fuzzy metrics. Fuzzy Sets and Systems. 162(1):91-93. https://doi.org/10.1016/j.fss.2010.09.017S9193162

Uncertainty quantification for random parabolic equations with non-homogeneous boundary conditions on a bounded domain via the approximation of the probability density function

[EN] This paper deals with the randomized heat equation defined on a general bounded interval [L-1, L-2] and with nonhomogeneous boundary conditions. The solution is a stochastic process that can be related, via changes of variable, with the solution stochastic process of the random heat equation defined on [0,1] with homogeneous boundary conditions. Results in the extant literature establish conditions under which the probability density function of the solution process to the random heat equation on [0,1] with homogeneous boundary conditions can be approximated. Via the changes of variable and the Random Variable Transformation technique, we set mild conditions under which the probability density function of the solution process to the random heat equation on a general bounded interval [L-1, L-2] and with nonhomogeneous boundary conditions can be approximated uniformly or pointwise. Furthermore, we provide sufficient conditions in order that the expectation and the variance of the solution stochastic process can be computed from the proposed approximations of the probability density function. Numerical examples are performed in the case that the initial condition process has a certain Karhunen-Loeve expansion, being Gaussian and non-Gaussian.This work has been supported by Spanish Ministerio de Economía y Competitividad grant MTM2017 89664 P. The author Marc Jornet acknowledges the doctorate scholarship granted by Programa de Ayudas de Investigación y Desarrollo (PAID), Universitat Politècnica de València.Calatayud-Gregori, J.; Cortés, J.; Jornet-Sanz, M. (2019). Uncertainty quantification for random parabolic equations with non-homogeneous boundary conditions on a bounded domain via the approximation of the probability density function. Mathematical Methods in the Applied Sciences. 42(17):5649-5667. https://doi.org/10.1002/mma.5333S564956674217Holden, H., Øksendal, B., Ubøe, J., & Zhang, T. (2010). Stochastic Partial Differential Equations. doi:10.1007/978-0-387-89488-1Casabán, M.-C., Company, R., Cortés, J.-C., & Jódar, L. (2014). Solving the random diffusion model in an infinite medium: A mean square approach. Applied Mathematical Modelling, 38(24), 5922-5933. doi:10.1016/j.apm.2014.04.063Xu, Z., Tipireddy, R., & Lin, G. (2016). Analytical approximation and numerical studies of one-dimensional elliptic equation with random coefficients. Applied Mathematical Modelling, 40(9-10), 5542-5559. doi:10.1016/j.apm.2015.12.041CalatayudJ CortésJC JornetM.On the approximation of the probability density function of the randomized heat equation.https://arxiv.org/pdf/1802.04190.pdfStrand, J. . (1970). Random ordinary differential equations. Journal of Differential Equations, 7(3), 538-553. doi:10.1016/0022-0396(70)90100-2Vaart, A. W. van der. (1998). Asymptotic Statistics. doi:10.1017/cbo9780511802256Villafuerte, L., Braumann, C. A., Cortés, J.-C., & Jódar, L. (2010). Random differential operational calculus: Theory and applications. Computers & Mathematics with Applications, 59(1), 115-125. doi:10.1016/j.camwa.2009.08.061Pitman, J. (1993). Probability. doi:10.1007/978-1-4612-4374-8Williams, D. (1991). Probability with Martingales. doi:10.1017/cbo9780511813658LawlessJF.Truncated Distributions: Wiley StatsRef: Statistics Reference Online;2014

Lp-calculus approach to the random autonomous linear differential equation with discrete delay

[EN] In this paper, we provide a full probabilistic study of the random autonomous linear differential equation with discrete delay , with initial condition x(t)=g(t), -t0. The coefficients a and b are assumed to be random variables, while the initial condition g(t) is taken as a stochastic process. Using Lp-calculus, we prove that, under certain conditions, the deterministic solution constructed with the method of steps that involves the delayed exponential function is an Lp-solution too. An analysis of Lp-convergence when the delay tends to 0 is also performed in detail.This work has been supported by the Spanish Ministerio de Economia y Competitividad Grant MTM2017-89664-P. The author Marc Jornet acknowledges the doctorate scholarship granted by Programa de Ayudas de Investigacion y Desarrollo (PAID), Universitat Politecnica de Valencia.Calatayud-Gregori, J.; Cortés, J.; Jornet-Sanz, M. (2019). Lp-calculus approach to the random autonomous linear differential equation with discrete delay. Mediterranean Journal of Mathematics. 16(4):1-17. https://doi.org/10.1007/s00009-019-1370-6S117164Smith, H.: An Introduction to Delay Differential Equations with Applications to the Life Sciences, Texts in Applied Mathematics. Springer, New York (2011)Driver, Y.: Ordinary and Delay Differential Equations. Applied Mathematical Science Series. Springer, New York (1977)Kuang, Y.: Delay Differential Equations: with Applications in Population Dynamics. Academic Press, Cambridge (2012)Bocharov, G.A., Rihan, F.A.: Numerical modelling in biosciences using delay differential equations. J. Comput. Appl. Math. 125, 183–199 (2000). https://doi.org/10.1016/S0377-0427(00)00468-4Jackson, M., Chen-Charpentier, B.M.: Modeling plant virus propagation with delays. J. Comput. Appl. Math. 309, 611–621 (2017). https://doi.org/10.1016/j.cam.2016.04.024Chen-Charpentier, B.M., Diakite, I.: A mathematical model of bone remodeling with delays. J. Comput. Appl. Math. 291, 76–84 (2016). https://doi.org/10.1016/j.cam.2017.01.005Erneux, T.: Applied Delay Differential Equations, Surveys and Tutorials in the Applied Mathematical Sciences Series. Springer, New York (2009)Kyrychko, Y.N., Hogan, S.J.: On the Use of delay equations in engineering applications. J. Vib. Control 16(7–8), 943–960 (2017). https://doi.org/10.1177/1077546309341100Matsumoto, A., Szidarovszky, F.: Delay Differential Nonlinear Economic Models (in Nonlinear Dynamics in Economics, Finance and the Social Sciences), 195–214. Springer-Verlag, Berlin Heidelberg (2010)Harding, L., Neamtu, M.: A dynamic model of unemployment with migration and delayed policy intervention. Comput. Econ. 51(3), 427–462 (2018). https://doi.org/10.1007/s10614-016-9610-3Oksendal, B.: Stochastic Differential Equations. Springer, New York (1998)Shaikhet, L.: Lyapunov Functionals and Stability of Stochastic Functional Differential Equations. Springer, New York (2013)Hartung, F., Pituk, M.: Recent Advances in Delay Differential and Differences Equations. Springer-Verlag, Berlin Heidelberg (2014)Shaikhet, L.: Stability of equilibrium states of a nonlinear delay differential equation with stochastic perturbations. Int. J. Robust Nonlinear Control 27(6), 915–924 (2016). https://doi.org/10.1002/rnc.3605Shaikhet, L.: About some asymptotic properties of solution of stochastic delay differential equation with a logarithmic nonlinearity. Funct. Differ. Equ. 4(1–2), 57–67 (2017)Fridman, E., Shaikhet, L.: Delay-induced stability of vector second-order systems via simple Lyapunov functionals. Automatica 74, 288–296 (2016). https://doi.org/10.1016/j.automatica.2016.07.034Benhadri, M., Zeghdoudi, H.: Mean square asymptotic stability in nonlinear stochastic neutral Volterra-Levin equations with Poisson jumps and variable delays. Functiones et Approximatio Commentarii Mathematici 58(2), 157–176 (2018). https://doi.org/10.7169/facm/1657Nouri, K., Ranjbar, H.: Improved Euler-Maruyama method for numerical solution of the Itô stochastic differential systems by composite previous-current-step idea. Mediterr. J. Math. 15, 140 (2018). https://doi.org/10.1007/s00009-018-1187-8Santonja, F., Shaikhet, L.: Probabilistic stability analysis of social obesity epidemic by a delayed stochastic model. Nonlinear Anal. Real World Appl. 17, 114–125 (2014). https://doi.org/10.1016/j.nonrwa.2013.10.010Santonja, F., Shaikhet, L.: Analysing social epidemics by delayed stochastic models. Discret. Dyn. Nat. Soc. 2012, 13 (2012). https://doi.org/10.1155/2012/530472 . (Article ID 530472)Liu, L., Caraballo, T.: Analysis of a stochastic 2D-Navier-Stokes model with infinite delay. J. Dyn. Differ. Equ. pp 1–26 (2018). https://doi.org/10.1007/s10884-018-9703-xCaraballo, T., Colucci, R., Guerrini, L.: On a predator prey model with nonlinear harvesting and distributed delay. Commun. Pure Appl. Anal. 17(6), 2703–2727 (2018). https://doi.org/10.3934/cpaa.2018128Smith, R.C.: Uncertainty Quantification. Theory, Implementation and Applications. SIAM, Philadelphia (2014)Soong, T.T.: Random Differential Equations in Science and Engineering. Academic Press, New York (1973)Nouri, K., Ranjbar, H.: Mean square convergence of the numerical solution of random differential equations. Mediterr. J. Math. 12(3), 1123–1140 (2015). https://doi.org/10.1007/s00009-014-0452-8Zhou, T.: A stochastic collocation method for delay differential equations with random input. Adv. Appl. Math. Mech. 6(4), 403–418 (2014). https://doi.org/10.4208/aamm.2012.m38Shi, W., Zhang, C.: Generalized polynomial chaos for nonlinear random delay differential equations. Appl. Numer. Math. 115, 16–31 (2017). https://doi.org/10.1016/j.apnum.2016.12.004Lupulescu, V., Abbas, U.: Fuzzy delay differential equations. Fuzzy Optim. Decis. Mak. 11(1), 91–111 (2012). https://doi.org/10.1007/s10700-011-9112-7Liu, S., Debbouche, A., Wang, J.R.: Fuzzy delay differential equations. On the iterative learning control for stochastic impulsive differential equations with randomly varying trial lengths. J. Comput. Appl. Math. 312, 47–57 (2017). https://doi.org/10.1016/j.cam.2015.10.028Krapivsky, P.L., Luck, J.L., Mallick, K.: On stochastic differential equations with random delay. J. Stat. Mech. Theory Exp. (2011). https://doi.org/10.1088/1742-5468/2011/10/P10008Garrido-Atienza, M.J., Ogrowsky, A., Schmalfuss, B.: Random differential equations with random delays. Stoch. Dyn. 11(2–3), 369–388 (2011). https://doi.org/10.1142/S0219493711003358Khusainov, D.Y., Ivanov, A.F., Kovarzh, I.V.: Solution of one heat equation with delay. Nonlinear Oscil. 12, 260–282 (2009). https://doi.org/10.1007/s11072-009-0075-3Asl, F.M., Ulsoy, A.G.: Analysis of a system of linear delay differential equations. J. Dyn. Syst. Meas. Control 125, 215–223 (2003). https://doi.org/10.1115/1.1568121Kyrychko, Y.N., Hogan, S.J.: On the use of delay equations in engineering applications. J. Vib. Control 16(7–8), 943–960 (2010). https://doi.org/10.1177/1077546309341100Villafuerte, L., Braumann, C.A., Cortés, J.C., Jódar, L.: Random differential operational calculus: theory and applications. Comput. Math. Appl. 59(1), 115–125 (2010). https://doi.org/10.1016/j.camwa.2009.08.061Strand, J.L.: Random ordinary differential equations. J. Diff. Equ. 7(3), 538–553 (1970). https://doi.org/10.1016/0022-0396(70)90100-2Khusainov, D.Y., Pokojovy, M.: Solving the linear 1d thermoelasticity equations with pure delay. Int. J. Math. Math. Sci. 2015, 1–11 (2015). https://doi.org/10.1155/2015/47926

Approximate solutions of randomized non-autonomous complete linear differential equations via probability density functions

[EN] Solving a random differential equation means to obtain an exact or approximate expression for the solution stochastic process, and to compute its statistical properties, mainly the mean and the variance functions. However, a major challenge is the computation of the probability density function of the solution. In this article we construct reliable approximations of the probability density function to the randomized non-autonomous complete linear differential equation by assuming that the diffusion coefficient and the source term are stochastic processes and the initial condition is a random variable. The key tools to construct these approximations are the random variable transformation technique and Karhunen-Loeve expansions. The study is divided into a large number of cases with a double aim: firstly, to extend the available results in the extant literature and, secondly, to embrace as many practical situations as possible. Finally, a wide variety of numerical experiments illustrate the potentiality of our findings.This work has been supported by the Spanish Ministerio de Economía y Competitividad grant MTM2017-89664-P. The author Marc Jornet acknowledges the doctorate scholarship granted by Programa de Ayudas de Investigación y Desarrollo (PAID), Universitat Politècnica de València.Calatayud-Gregori, J.; Cortés, J.; Jornet-Sanz, M. (2019). Approximate solutions of randomized non-autonomous complete linear differential equations via probability density functions. Electronic Journal of Differential Equations. 2019:1-40. http://hdl.handle.net/10251/139661S140201

Random differential equations with discrete delay

[EN] In this article, we study random differential equations with discrete delay with initial condition The uncertainty in the problem is reflected via the outcome omega. The initial condition g(t) is a stochastic process. The term x(t) is a stochastic process that solves the random differential equation with delay in a probabilistic sense. In our case, we use the random calculus approach. We extend the classical Picard theorem for deterministic ordinary differential equations to calculus for random differential equations with delay, via Banach fixed-point theorem. We also relate solutions with sample-path solutions. Finally, we utilize the theoretical ideas to solve the random autonomous linear differential equation with discrete delay.This work has been supported by the Spanish Ministerio de Economía y Competitividad grant MTM2017 89664 PCalatayud-Gregori, J.; Cortés, J.; Jornet-Sanz, M. (2019). Random differential equations with discrete delay. Stochastic Analysis and Applications. 37(5):699-707. https://doi.org/10.1080/07362994.2019.1608833S699707375Fridman, E., & Shaikhet, L. (2017). Stabilization by using artificial delays: An LMI approach. Automatica, 81, 429-437. doi:10.1016/j.automatica.2017.04.015Shaikhet, L., & Korobeinikov, A. (2015). Stability of a stochastic model for HIV-1 dynamics within a host. Applicable Analysis, 95(6), 1228-1238. doi:10.1080/00036811.2015.1058363Caraballo, T., Colucci, R., & Guerrini, L. (2018). On a predator prey model with nonlinear harvesting and distributed delay. Communications on Pure & Applied Analysis, 17(6), 2703-2727. doi:10.3934/cpaa.2018128Caraballo, T., J. Garrido-Atienza, M., Schmalfuss, B., & Valero, J. (2017). Attractors for a random evolution equation with infinite memory: Theoretical results. Discrete & Continuous Dynamical Systems - B, 22(5), 1779-1800. doi:10.3934/dcdsb.2017106Krapivsky, P. L., Luck, J. M., & Mallick, K. (2011). On stochastic differential equations with random delay. Journal of Statistical Mechanics: Theory and Experiment, 2011(10), P10008. doi:10.1088/1742-5468/2011/10/p10008Liu, S., Debbouche, A., & Wang, J. (2017). On the iterative learning control for stochastic impulsive differential equations with randomly varying trial lengths. Journal of Computational and Applied Mathematics, 312, 47-57. doi:10.1016/j.cam.2015.10.028Dorini, F. A., Cecconello, M. S., & Dorini, L. B. (2016). On the logistic equation subject to uncertainties in the environmental carrying capacity and initial population density. Communications in Nonlinear Science and Numerical Simulation, 33, 160-173. doi:10.1016/j.cnsns.2015.09.009Slama, H., El-Bedwhey, N. A., El-Depsy, A., & Selim, M. M. (2017). Solution of the finite Milne problem in stochastic media with RVT Technique. The European Physical Journal Plus, 132(12). doi:10.1140/epjp/i2017-11763-6Nouri, K., Ranjbar, H., & Torkzadeh, L. (2019). Modified stochastic theta methods by ODEs solvers for stochastic differential equations. Communications in Nonlinear Science and Numerical Simulation, 68, 336-346. doi:10.1016/j.cnsns.2018.08.013Lupulescu, V., O’Regan, D., & ur Rahman, G. (2014). Existence results for random fractional differential equations. Opuscula Mathematica, 34(4), 813. doi:10.7494/opmath.2014.34.4.813Strand, J. . (1970). Random ordinary differential equations. Journal of Differential Equations, 7(3), 538-553. doi:10.1016/0022-0396(70)90100-2Villafuerte, L., Braumann, C. A., Cortés, J.-C., & Jódar, L. (2010). Random differential operational calculus: Theory and applications. Computers & Mathematics with Applications, 59(1), 115-125. doi:10.1016/j.camwa.2009.08.061Granas, A., & Dugundji, J. (2003). Fixed Point Theory. Springer Monographs in Mathematics. doi:10.1007/978-0-387-21593-

The damped pendulum random differential equation: A comprehensive stochastic analysis via the computation of the probability density function

[EN] This paper deals with the damped pendulum random differential equation: (X) over double dot(t)+2 omega(0)xi(X) over dot(t) + omega X-2(0)(t) = Y(t), t is an element of [0, T], with initial conditions X(0) = X-0 and (X) over dot(0) = X-1. The forcing term Y(t) is a stochastic process and X-0 and X-1 are random variables in a common underlying complete probability space (Omega, F, P). The term X(t) is a stochastic process that solves the random differential equation in both the sample path and in the L-P senses. To understand the probabilistic behavior of X(t), we need its joint finite-dimensional distributions. We establish mild conditions under which X(t) is an absolutely continuous random variable, for each t, and we find its probability density function f(X(t))(x). Thus, we obtain the first finite-dimensional distributions. In practice, we deal with two types of forcing term: Y(t) is a Gaussian process, which occurs with the damped pendulum stochastic differential equation of Ito type; and Y(t) can be approximated by a sequence {Y-N(t)}(N-1)(infinity) in L-2([0, T] x Omega), which occurs with Karhunen-Loeve expansions and some random power series. Finally, we provide numerical examples in which we choose specific random variables X-0 and X-1 and a specific stochastic process Y(t), and then, we find the probability density function of X(t). (C) 2018 Elsevier B.V. All rights reserved.This work has been supported by the Spanish Ministerio de Economia y Competitividad grant MTM2017-89664-P. Marc Jornet acknowledges the doctorate scholarship granted by Programa de Ayudas de Investigacion y Desarrollo (PAID), Universitat Politecnica de Valencia. The authors are grateful for the valuable comments raised by the reviewers that have improved the final version of the paper.Calatayud-Gregori, J.; Cortés, J.; Jornet-Sanz, M. (2018). The damped pendulum random differential equation: A comprehensive stochastic analysis via the computation of the probability density function. Physica A Statistical Mechanics and its Applications. 512:261-279. https://doi.org/10.1016/j.physa.2018.08.024S26127951